How to Find GCF of 643/38, 269/49, 406/14?

GCF of 643/38, 269/49, 406/14

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 643/38, 269/49, 406/14 i.e 1/1862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 643/38, 269/49, 406/14.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 643/38,269/49,406/14?

Given fractions are 643/38,269/49,406/14

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 643/38,269/49,406/14, numerators are 643,269,406

Denominators are 38,49,14

The GCF of 643,269,406 is 1 .

LCM of 38,49,14 is 1862.

The greatest common factor of 643/38,269/49,406/14 = [GCF of 643,269,406]/[LCM of 38,49,14]= 1/1862

Therefore, the GCF of 643/38,269/49,406/14 is 1/1862.

Greatest Common Factor of 643,269,406

To find the highest common factor of 643,269,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 643 are 1, 643

The factors of 269 are 1, 269

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 643,269,406 is 1.

Lets's calculate GCF of 643,269,406

Greatest Common Factor (GCF) of 643,269,406 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 643,269,406 By Matching Biggest Common Factor Method

Now, list down the factors of 643

1,643

Now, list down the factors of 269

1,269

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 643,269,406 . The biggest common factor number is the GCF number.
So the greatest common factor 643,269,406 is 1.

Lets's calculate LCM of 38,49,14

Lowest Common Multiple of 38,49,14 using Common Division

2	38, 49, 14
7	19, 49, 7
	19, 1, 7

∴ So the LCM of the given numbers is 2 x 7 x 19 x 1 x 7 = 1862

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1862

Therefore, the GCF of Fractions 643/38,269/49,406/14 is 1/1862

Least Common Multiple of 38,49,14 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 38,49,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,49,14) = 1

common factors(in case of two or more numbers have common factors) = 14

GCF(38,49,14) x common factors =1 x 14 = 14

LCM(38,49,14) = ( 38 × 49 × 14 ) / 14

LCM(38,49,14) = 26068 / 14

LCM(38,49,14) = 1862

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FAQs on GCF of Fractions of 643/38, 269/49, 406/14

1. What is the HCF of 643,269,406?

The HCF of 643,269,406 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 643/38, 269/49, 406/14?

Answer: GCF of Numerators as per given numbers 643/38, 269/49, 406/14 is

GCF of Numerators i.e. for 643,269,406 is 1

LCM of denominators i.e. for 38,49,14 is 1862.

Thus, GCF of Fractions is 1/1862.Finally, GCF of Fractions for 643/38, 269/49, 406/14 is 1/1862.